Cosmological Simulations Using Particle - Mesh

The purpose of cosmological simulations is to model the growth of structure in the universe. The techniques described here model the mass density of the universe with a distribution of softened particles. Evolution is simulated by following the trajectories of these particles under their mutual gravity. Since the region of the universe modelled is typically very much smaller than the horizon volume, Newtonian equations of motion are adequate to describe the particle dynamics and evolution of structure. The resulting numerical schemes are straightforward and robust. An alternative approach is to describe the mass distribution as a uid and calculate the evolution from the appropriate uid equations (e.g., Peebles 1987). A number of other analytic and semi-analytic approaches to gravitational evolution have been discussed. The description of the growth of small perturbations in the matter distribution is well established, both to rst order and at higher orders (see, for example, Peebles 1980). Many observational constraints, however, are the result of highly non-linear gravitational evolution for which perturbation analysis is of limited use. Numerical N-body techniques ooer a simple and eeective tool for investigating non-linear cosmological gravita-tional evolution. Many of the results arising from potential theory and the theory of gravitating systems of particles, as discussed in this volume and elsewhere, are directly applicable to the cosmological situation and will not be addressed here in further detail. The principal features peculiar to cosmologi-cal simulations arise from the construction of an initial particle distribution, the necessity of describing evolution in an expanding cosmic background and the choice of suitable boundary conditions. The remainder of the introduction addresses these issues and describes the popular mesh-based